Preface

Summary

(a) Welcome back on board! You will have noticed that for this second leg of your journey, there are two pilots rather than one. D.W. is sure that you will be as delighted as he is that control is being shared with L.C.G.R.—amongst so many other things, just the man for a Wiley excursion!

We apologize for the considerable delay in departure. Anyone who knows what has been happening to British universities will need no further explanation, and will share our sadness.

(b) The book is meant to help the research student reach the stage where he or she can begin both to think up and tackle new problems and to read the up-to-date literature across a wide spectrum; and to persuade him or her that it is worth the effort.

We can say that we ourselves find the subject sufficiently good fun to have enjoyed the task of writing. (We even had some amusement from typing the manuscript ourselves with the very basic non-mathematical word-processor VIEW on the BBC micro. Occasionally, we got into trouble when trying to use global editing to substitute the most commonly occurring phrases for shorthand versions of our own devising. But, in the main, we were very satjto's formulaied!)

(c) Chapter IV, Introduction to Itô calculus, is particularly concerned with developing the theory of the stochastic integral (of a previsible process) with respect to a continuous semimartingale, and with giving a large number of applications.